Jing Liu

Publications

6 Dependent Weighted Aggregation Operators of Hesitant Fuzzy Numbers

Authors: Jing Liu

Abstract:

In this paper, motivated by the ideas of dependent weighted aggregation operators, we develop some new hesitant fuzzy dependent weighted aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy numbers rather than exact numbers, or intervals. In fact, we propose three hesitant fuzzy dependent weighted averaging(HFDWA) operators, and three hesitant fuzzy dependent weighted geometric(HFDWG) operators based on different weight vectors, and the most prominent characteristic of these operators is that the associated weights only depend on the aggregated hesitant fuzzy numbers and can relieve the influence of unfair hesitant fuzzy numbers on the aggregated results by assigning low weights to those “false” and “biased” ones. Some examples are given to illustrated the efficiency of the proposed operators.

Keywords: Hesitant fuzzy numbers, hesitant fuzzy dependent weighted averaging(HFDWA) operators, hesitant fuzzy dependent weighted geometric(HFDWG) operators

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5 Proximal Parallel Alternating Direction Method for Monotone Structured Variational Inequalities

Authors: Min Sun, Jing Liu

Abstract:

In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.

Keywords: global convergence, structured variational inequalities, proximal point method

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4 Inexact Alternating Direction Method for Variational Inequality Problems with Linear Equality Constraints

Authors: Min Sun, Jing Liu

Abstract:

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.

Keywords: global convergence, variational inequality problems, alternating direction method

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3 A Family of Entropies on Interval-valued Intuitionistic Fuzzy Sets and Their Applications in Multiple Attribute Decision Making

Authors: Min Sun, Jing Liu

Abstract:

The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFS. Firstly, we propose a family of entropies on IvIFS with a parameter λ ∈ [0, 1], which generalize two entropy measures defined independently by Zhang and Wei, for IvIFS, and then we prove that the new entropy is an increasing function with respect to the parameter λ. Furthermore, a new multiple attribute decision making (MADM) method using entropy-based attribute weights is proposed to deal with the decision making situations where the alternatives on attributes are expressed by IvIFS and the attribute weights information is unknown. Finally, a numerical example is given to illustrate the applications of the proposed method.

Keywords: Multiple Attribute Decision Making, Interval-valued Intuitionistic Fuzzy Sets, intervalvalued intuitionistic fuzzy entropy

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2 A Systems Approach to Gene Ranking from DNA Microarray Data of Cervical Cancer

Authors: Frank Emmert Streib, Matthias Dehmer, Jing Liu, Max Mühlhauser

Abstract:

In this paper we present a method for gene ranking from DNA microarray data. More precisely, we calculate the correlation networks, which are unweighted and undirected graphs, from microarray data of cervical cancer whereas each network represents a tissue of a certain tumor stage and each node in the network represents a gene. From these networks we extract one tree for each gene by a local decomposition of the correlation network. The interpretation of a tree is that it represents the n-nearest neighbor genes on the n-th level of a tree, measured by the Dijkstra distance, and, hence, gives the local embedding of a gene within the correlation network. For the obtained trees we measure the pairwise similarity between trees rooted by the same gene from normal to cancerous tissues. This evaluates the modification of the tree topology due to progression of the tumor. Finally, we rank the obtained similarity values from all tissue comparisons and select the top ranked genes. For these genes the local neighborhood in the correlation networks changes most between normal and cancerous tissues. As a result we find that the top ranked genes are candidates suspected to be involved in tumor growth and, hence, indicates that our method captures essential information from the underlying DNA microarray data of cervical cancer.

Keywords: Cancer, graph similarity, DNA microarray data

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1 Ranking Genes from DNA Microarray Data of Cervical Cancer by a local Tree Comparison

Authors: Frank Emmert-Streib, Matthias Dehmer, Jing Liu, Max Muhlhauser

Abstract:

The major objective of this paper is to introduce a new method to select genes from DNA microarray data. As criterion to select genes we suggest to measure the local changes in the correlation graph of each gene and to select those genes whose local changes are largest. More precisely, we calculate the correlation networks from DNA microarray data of cervical cancer whereas each network represents a tissue of a certain tumor stage and each node in the network represents a gene. From these networks we extract one tree for each gene by a local decomposition of the correlation network. The interpretation of a tree is that it represents the n-nearest neighbor genes on the n-th level of a tree, measured by the Dijkstra distance, and, hence, gives the local embedding of a gene within the correlation network. For the obtained trees we measure the pairwise similarity between trees rooted by the same gene from normal to cancerous tissues. This evaluates the modification of the tree topology due to tumor progression. Finally, we rank the obtained similarity values from all tissue comparisons and select the top ranked genes. For these genes the local neighborhood in the correlation networks changes most between normal and cancerous tissues. As a result we find that the top ranked genes are candidates suspected to be involved in tumor growth. This indicates that our method captures essential information from the underlying DNA microarray data of cervical cancer.

Keywords: Cervical Cancer, graph similarity, DNA microarray data, generalized trees, graph alignment

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